Solution of inverse heat conduction problem for determining heat input,weld shape,and grain structure during laser welding

Abstract

The technique of solving the inverse heat conduction problem to determine the steady state welding conditions corresponding to observable or desired weld features is outlined. The objective function includes calculated and experimental values of the temperature related functions, constraints, and regularisation of unknown parameters. The algorithm used to determine the minimum of the objective function is presented. As an example, the temperature field and its corresponding grain structure have been calculated taking into consideration the latent heat and fluid flow in the laser welding of two aluminium alloys. The weld width and texture orientation have been used as the temperature related functions. The results of the simulations are directly compared with the experimental evidence.

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References

Tikhonov

A. N.

and Arsenin

V. Y.

: ‘Solutions of ill-posed problems’; 1977, Washington, DC, V. H. Winston and Sons/New York, Wiley.

Kozdoba

L. A.

and Krukovsky

P. G.

: ‘Methods of solution to inverse heat transfer problems’; 1982, Kiev, Ukraine, Naukova Dumka (in Russian).

Beck

J. V.

, Blackwell

, and St Clair

C. R.

: ‘Inverse heat conduction: ill-posed problems’; 1985, New York, Wiley-International.

Tikhonov

A. N.

, Kalner

V. D.

, and Glasko

V. B.

: ‘Mathematical modelling of technological processes and method of inverse problems in machinery’; 1990, Moscow, Machinostroenie (in Russian).

Tikhonov

A. N.

, Goncharsky

A. V.

, Stepanov

V. V.

, and Yagola

A. G.

: ‘Numerical methods of solution to ill-posed problems’; 1990, Moscow, Nauka (in Russian).

Alifanov

O. M.

: ‘Inverse heat transfer problems’; 1994, Berlin, Springer.

Tikhonov

A. N.

, Leonov

A. S.

, and Yagola

A. G.

: ‘Nonlinear ill-posed problems’; 1998, London, Chapman and Hall.

Beck

J. V.

: in ‘Mathematics of heat transfer’, (ed. G. E. Tupholme et al.), 13–24; 1998, Oxford, Clarendon Press.

Beck

J. V.

: in ‘Modeling of casting, welding and advanced solidification processes V’, (ed. M. Rappaz et al.), 503–514; 1991, Warrendale, PA, The Minerals, Metals and Materials Society.

10.

Zabaras

: in ‘Modeling of casting, welding and advanced solidification processes V’, (ed. M. Rappaz et al.), 523–530; 1991, Warrendale, PA, The Minerals, Metals and Materials Society.

11.

Karkhin

V. A.

, Ilyin

A. S.

, Plochikhine

V. V.

, and Bergmann

H. W.

: in Proc. 8th Conf. on ‘Laser materials processing in the Nordic countries’, (ed. F. O. Olsen and J. K. Kristensen), Copenhagen, August 2001, Technical University of Denmark/FORCE Institute, 289–300 (ISBN 87–90855–32–9/ISSN 1456–4491).

12.

Rappaz

, Desbiolles

J.-L.

, Drezet

J.-M.

, Ch.-A. Gandin, A. Jacot, and Ph. Thevoz: in ‘Modelling of casting, welding and advanced solidification processes VII’, (ed. M. Cross et al.), 449–457; 1995, Warrendale, PA, The Minerals, Metals and Materials Society.

13.

Bergmann

H. W.

, Mayer

, Mueller

, and Ploshikhin

V. V.

: in ‘Mathematical modelling of weld phenomena 4’, (ed. H. Cerjak), 166–183; 1998, London, The Institute of Materials.

14.

Rykalin

N. N.

: ‘Calculation of heat flow in welding’, (translated by Z. Paley and C. M. Adams Jr); 1951, Moscow, Mashgiz.

15.

Karkhin

V. A.

: ‘Thermal fundamentals of welding’; 1990, Leningrad, LGTU (Leningrad State Technical University) (in Russian).

16.

Ploshikhin

V. V.

and Bergmann

H. W.

: in ‘Mathematical modelling of weld phenomena 4’, (ed. H. Cerjak), 150–165; 1998, London, The Institute of Materials.

17.

Dausinger

: ‘Strahlwerkzeug Laser: Energeeinkopplung und Processeffektivitat’; 1995, Stuttgart, Teubner Verlag.